Anisotropy Parameters for the Effective Description of Crystalline Color Superconductors

Abstract

In the high density low temperature limit, Quantum Chromodynamics (QCD) exhibits a transition to a phase characterized by color superconductivity and by energy gaps in the fermion spectra. Under specific circumstances the gap parameter has a crystalline pattern, breaking translational and rotational invariance. The corresponding phase is the the crystalline color superconductive phase (or {\it LOFF} phase). In the effective theory the fermions couple to the phonon arising from the breaking of rotation and translation invariance. We compute the parameters of the low energy effective lagrangian describing the motion of the free phonon in the high density medium and derive the phonon dispersion law.